Solve frac{sqrt{15}}{sqrt{72}}

$$\frac{ \sqrt{ 15 } }{ \sqrt{ 72 } }$$

Evaluate

$$\frac{\sqrt{30}}{12}\approx 0.456435465$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{\sqrt{15}}{6\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{15}}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{15}\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{15}\sqrt{2}}{6\times 2}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\sqrt{30}}{12}$$